I bought a new wifi router, Linksys G, Model WRT54G2, it works fine for my desktop, but I have 2 work laptops and 1 personal laptop, they all have Vista on them, I cant get a wifi connection with any of them. They all have internal wifi cards.

Make sure the wifi adapters are physically enabled. There is usually a keyboard shortcut that is used to enable/disable the onboard network interface on notebooks. If your desktop is hard-wired to the router (mean direct connect/no wireless) make sure that the router is transmitting a G-signal and that there is no encryption set. You can configure the router's settings by typing "192.168.1.1" in your browser's address bar.

The laptops were working fine on my previous linksys router. My daughters desktop use an external wifi device, it picks it up fine and its faster than before, it also has Vista.

Vista can be cranky; use the Wireless Network Wizard to create the connection.
When it ask "Public or Private", click on the Private to open the firewall